During an overcooling transient in a pressurized water reactor, the cold water from the high-pressure safety system is injected into the hot primary coolant in the cold leg. This can cause the water temperature in the cold leg and downcomer annulus to decrease; hence, the problem of pressurized thermal shock arises. A multidimensional numerical study for the analysis of the Electric Power Research Institute/Creare one-fifth-scale mixing test is performed. A new, accurate, stable mass-flow-weighted skew-upwind scheme is employed in the finite difference solution of the energy equation. The temperature predictions using the new scheme are in good agreement with the experimental data. A significant reduction in the numerical diffusion errors was achieved. These errors have plagued the conventional upwind scheme results. A good agreement between the computed velocity patterns and flow visualization is obtained.